( 5 Ä 7 )

P s C p ~t

As c is to r, so is - = G B (by the 6. Pros.) to —— = G F, that is

rr r

as Radius to the Sine of Elevation, so the Parameter to the Line GF ; so theLines GF are as the Sines of Elevation, and the Times are proportional tothole Lines 3 wherefore the Times are as the Sines of Elevation: Ergo conßatPropositio.

Prop. IX. Prob. I.] A Projeflion being made, as you flease, having the Di-fiance and Altitudc, or Descent of an Object, througb which the Projeci passes ,together mth the Angle of Elevation of the Line of DireFtion , to find the Pa-rameter and Velocity 3 that is, (having the Angle FG B,) G M, and M X.

Solutions) As Radius to Secant of F G B, so GM the Distance given,to G L 3 and as Radius to Tangent of FG B, so G M to L-M ThenL M — MX in Heights, or -1- M X in Descent s 3 or eise MX — M L,if the DireFtion be Below the Horizontal-Line, is the Fall in the Time thatthe Direct Impulse given in G, would have carried the Project from G to L= L X = G Y 3 then by reason of the Parabola 3 as L X, or G Y, is toG L or Y X 3 so is G so, to the Parameter sought. To find the Velccityof the Impulse , by Prop. ~l. and 4. find the Time in Seconds that a Bodywould Fall the Spaee L X, and by that dividing the Line G L, the Quotewill be the Volccity, or Spaee Moved in a Second Sought, which is always aA lean Proportional between the Parameter and 16 Feer, 1 Inch.

Pröp. X. Prob. 2.J Having the Parameter, Horizontal Dißance, and Heightor Dcjcent of an Object, to find the Elcvations of the Lines of Direktion neeefsaryto Hit the given OtjeFl ; that is, having GM, MX, and the greatese Rän-dern equct to half the Parameter 3 to find the Angles FG B.

Let the Tangent of the Angle sought be — t, the Horizontal DistanceG M = b, the. Altitude of the Object MX — h, the Parameter =3: p, and

Radius — r, and it will be, as r to t, so b to — M L; and ql h

'Cin Aseents?£in Deseents^

rabola 3 but bb

— L X, and -— -j- p h — G L q.

X Y q. ratione Pa-

tt b b

=r. G L q. (47. i. Euclid.) Wherefore- t-Lds

4 - p h = b b 4 —-3 which Equation transposed, is-= ~ *

r r

_ t t p t _ p b

-h t h — bb 3 divided by b b, is-—-4--- — 1, This Equati-

r r b r b b

tron shews the Qiuestion to have two Anfwers, and the Roots thereof are —

Fi $. 172-